The invention is based on a fuel injection pump for internal combustion engines defined hereinafter. From U.S. Pat. No. 2,863,458, a fuel injection pump of this type is already known, in which the hydraulic supply onset adjusting device includes, inside the drive tappet, an adjusting piston which is subjected to the pressure of a control fluid source. The control fluid is delivered via a conduit arrangement having a delivery conduit in the pump housing and having, in addition to the delivery conduit discharging into a guide bore of the drive tappet, a radial connecting bore, drilled through the wall of the drive tappet, leading to the pressure chamber of the supply onset adjusting device. At bottom dead center of the pump piston, this connecting bore and the delivery conduit face one another, so that the control fluid, which is under control pressure, can flow into the pressure chamber inside the drive tappet. In this known apparatus, the pressure of the control fluid must overcome the biasing force of the tappet spring exerted upon the adjusting piston. Depending on how great the pressure of the fluid is, the adjusting piston and simultaneously the pump piston are lifted relative to the drive tappet, so that upon the next compression stroke, with the connection between the delivery conduit and the connecting bore having first been broken, an earlier supply onset on the part of the pump piston is brought about than if the pressure of the fluid had not lifted the adjusting piston. The fluid pressure must therefore overcome the biasing force of the tappet spring, which especially in high-speed injection pumps is very great. Accordingly, the pressure must be relatively high, which in turn causes sealing problems and leakage losses. A further disadvantage is that the highly stressed tappet spring inevitably relaxes after a certain period in operation, resulting in altered force ratios, which in turn cause a change in the characteristic of the supply onset adjusting device. The connecting point in the wall of the guide bore between the drive tappet and the pump housing, embodied as a control point, undergoes wear, especially if the pump housing is of aluminum, as is generally the case in in-line injection pumps. This wear is a further cause of leakage losses, and sufficiently severe wear also leads to disruptions in pump function It is accordingly the object of the invention to overcome the above disadvantages and to improve the function of the supply onset adjusting device.